The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm and that emitted by the North star has the maximum value at 350 nm. If these stars behave like black bodies, then the ratio of the surface temperatures of the sun and the north star is

Options

A. 1.46
B. 0.69
C. 1.21
D. 0.83

Answer

B

Explanation

From Wien's displacement law
`lambda_(m)T` = constant
`rArr lambda_(m_(1))T_(1) = lambda_(m_(2))T_(2)`
or `(T_(1))/(T_(2)) = (lambda_(m_(2)))/(lambda_(m_(1)))" "...(i)`
Hence, `lambda_(m_(1)) = 510 nm " "lambda_(m_(2)) = 350 nm`
So, on putting these values in Eq. (i)
`(T_(1))/(T_(2)) = (350)/(510)`
`rArr (T_(1))/(T_(2)) = (35)/(51) = 0.6862 ~~ 0.69`